2015/10/13 by Marino Badiale, Badiale, Marino, Michela Guida +3 · 3 citations
Computer Science · Mathematics · #35J20 (Secondary) #35J92 #46E30 #46E35 (Primary) #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #math.AP #math.FA #msc:35J20 #msc:35J92 #msc:46E30 #msc:46E35
paper · pdf · doi:10.48550/arxiv.1510.03879
arXiv admin note: substantial text overlap with arXiv:1403.3803
arxiv created 2015/10/13 · openalex publication_date 2015/10/13 · arxiv updated 2015/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given 1<p<N and two measurable functions V(r)≥ 0 and K(r)>0, r>0, we define the weighted spaces W=\ u∈ D1,p(ℝN):∫ℝNV(|x|) |u|p dx<∞ \ , LKq =Lq(ℝN,K( | x| ) dx) and study the compact embeddings of the radial subspace of W into LKq1+LKq2, and thus into LKq (=LKq+LKq) as a particular case. Both exponents q1,q2,q greater and lower than p are considered. Our results do not require any compatibility between how the potentials V and K behave at the origin and at infinity, and essentially rely on power type estimates of their relative growth, not of the potentials separately.